Trying to animate an extrude in 3D using curves generated by an equation over time
A way to make the impeller to appear to grow like a shell is to use Boolean operations between a shape and the Lily impeller. The animation below shows an intersection between a cone and an the impeller.

Steps to recreate.

Import/create the lily impeller.
Add a cone that roughly matches the angle of the lily impeller spiral and large enough to contain the full impeller.

Animate the cone moving from the above the impeller until it fully encloses the impeller. This will generate the animation above.

The geometry for the impeller above was from  https://www.thingiverse.com/thing:956458 modeled after Jay Harmans drawings, courtesy of yzorg.